I applaud your enthusiasm, but suspect that you're heading off in the wrong direction! These lapidary tumblers (coupled with your suggestion of the use of a grinder) don't give the end result that you see some of us regularly using in the forum. Grinders generally operate at too high a speed, causing excessive heat and friction, which shatters most stone, whereas lapidary saws usually have a water cooled, diamond grit blade and operate at slow speed. The type of cabochon that I use regularly is pre-cut on the saw to a "coin", with one flat surface being glued with epoxy onto a stub (a bit like a short length of broom-stick), and then shaped and polished against water-fed stones and buffers to achieve the rounded over shape and finish.
All of this is slow, labour intensive work and tends to happen in less-developed countries where labour costs are low. I've had a limited amount of success in cutting and polishing my own cabochons, but only in slate, which is a relatively soft stone, and that took many failed attempts before I found successful strategies for working it.
Sorry to be so negative when you sound so enthusiastic, but better that you know what you're heading into!
Les